How should leaders balance accountability with backlash after tone-deaf campaigns?

[Madison12]

I'm a mid-level manager in the tech industry, and our company recently faced a significant internal and external backlash over a tone-deaf marketing campaign, leading to calls for specific individuals to be fired—a situation that feels squarely in the realm of cancel culture. As someone who needs to help navigate the fallout and guide my team, I'm struggling to find a principled approach that addresses legitimate criticism without capitulating to mob mentality or destroying careers over mistakes. For other leaders who have dealt with similar public relations crises, how did you separate constructive accountability from punitive overreach? What processes did you implement to investigate, respond, and ultimately repair trust, both internally with employees and externally with your customer base?